如何檢查表示數字的對象是否大於另一個對象？

Question

我目前正在編寫一個可以表示無限大數量的類（理論上）。 此類的構造函數從字符串值創建對象，這就是為什么數字可能很大但未知的原因。

我之所以開始寫這堂課，是因為我希望能夠編寫一個程序，該程序能夠以任意大的數量執行數學計算。 因此，我開始編寫一個可以很好地處理整數，浮點數，雙精度數（希望是十進制）等標准范圍內的值的類。

這是該類的聲明和主要構造函數：

/// <summary>
/// Creates a new instance of the LargeDecimal class, which represents either a whole or decimal number.
/// </summary>
/// <param name="number">The string representation of the number.</param>
public LargeDecimal(string value)
{
    string number = value.Replace(" ", "");
    if (number.Contains("-") && (number.IndexOf('-') == 0)) {
        number = number.Replace("-", "");
        IsNegative = true;
    }
    // Determining whether the number is whole or contains a decimal.
    if (number.IndexOf('.') == -1) {
        // Does not contain a decimal.
        for (int i = 0; i < number.Length; i++)
            wholeDigits.Add(int.Parse(number[i].ToString()));
        IsWhole = true;
    }
    else {
        // Still check if number is whole. Add all decimal digits.
        string[] numArray = number.Split('.');
        int sumOfDecimalDigits = 0;
        for (int i = 0; i < numArray[1].ToString().Length; i++)
            sumOfDecimalDigits += int.Parse(numArray[1].ToString()[i].ToString());
        if (sumOfDecimalDigits <= 0) {
            // Is a whole number.
            for (int i = 0; i < numArray[0].ToString().Length; i++)
                wholeDigits.Add(int.Parse(numArray[0].ToString()[i].ToString()));
            IsWhole = true;
        }
        else {
            // Is not a whole number.
            for (int i = 0; i < numArray[0].ToString().Length; i++)
                wholeDigits.Add(int.Parse(numArray[0].ToString()[i].ToString()));
            for (int i = 0; i < numArray[1].ToString().Length; i++)
                decimalDigits.Add(int.Parse(numArray[1].ToString()[i].ToString()));
            IsWhole = false;
        }
    }
}

該類基本上是通過兩個類型為int的列表表示數字的方法，其中一個列表代表組成數字整個分區的數字，另一個列表代表組成數字的十進制分區的數字（如果適用）。

我已經編寫了一個Add方法，該方法接受兩個LargeDecimal對象，將它們的值相加，然后返回一個新的LargeDecimal對象，其總和為它的值。 盡管不完整，但它確實適用於LargeDecimal對象，這些對象僅是整數，並且都是正數或都是負數（圖片！）。

我已經意識到，添加用於比較兩個值（大於/小於/等於）的方法在計算中非常有用。 但是，我不確定如何檢查LargeDecimal對象的值是大於還是小於另一個LargeDecimal的值。

在某些情況下，我只能比較WholeDigits列表中的項目數量，但這僅是當兩個值的項目數量都不同時。 我不確定如何比較兩個數字，例如：15498765423654973246和15499111137583924246。

而且我認為，如果我嘗試比較兩個小數部分，將會變得更加困難：8573819351.86931和8573809999.85999

我不希望將整數計算與位置值一起使用（例如，在數字831中，數字8的值為8 * 100，數字3的值為3 * 10，數字1的值為1 * 1），因為我希望此類能夠表示任何給定大小，長度和范圍的值（而int不能處理最大2147483647的值）。

任何對此的幫助將不勝感激！ 謝謝你們！

Answer 1

假設此實現看起來像這樣：

List<int> WholeList;
List<int> FactionalList;
bool IsNegative;

並且它們都遠離小數點增長，那么比較算法將像這樣

1. 首先比較跡象。 負面總是小於正面。
2. 比較WholeList的長度，較長的則具有較大的大小（較大的數字取決於符號）
3. 如果WholeList.Count相同。 比較從最高有效位開始的每個數字（首先是WholeList [Count-1]），首先比較數字之間的差異將確定較大的幅度。
4. 如果將其放入FractionalList，然后在一個列表中用完數字。 FractionalList較長的數字將具有更大的幅度。

Answer 2

我將從實現IComparable開始：

public class LargeDecimal : IComparable<LargeDecimal>

實現看起來像：

public int CompareTo(LargeDecimal other)
{
    if (other == null) return 1;
    if (ReferenceEquals(this, other)) return 0;

    if (IsNegative != other.IsNegative)
    {
        if (other.IsNegative) return 1;
        return -1;
    }

    int multiplier = (IsNegative) ? -1 : 1;

    if (wholeDigits.Count > other.wholeDigits.Count) return 1 * multiplier;
    if (wholeDigits.Count < other.wholeDigits.Count) return -1 * multiplier;

    for (int i = 0; i < wholeDigits.Count; i++)
    {
        if (wholeDigits[i] > other.wholeDigits[i]) return 1 * multiplier;
        if (wholeDigits[i] < other.wholeDigits[i]) return -1 * multiplier;
    }

    for (int i = 0; i < Math.Min(decimalDigits.Count, other.decimalDigits.Count); i++)
    {
        if (decimalDigits[i] > other.decimalDigits[i]) return 1 * multiplier;
        if (decimalDigits[i] < other.decimalDigits[i]) return -1 * multiplier;
    }

    if (decimalDigits.Count > other.decimalDigits.Count) return 1 * multiplier;
    if (decimalDigits.Count < other.decimalDigits.Count) return -1 * multiplier;

    return 0;
}

更新資料

這個項目是在今晚的晚餐上坐在我的大腦上的，所以我又去了一些有趣的事情。 不確定這是否有幫助，但想知道我會分享我的想法。

首先，我添加了一些字段來使類實際起作用：

public bool IsNegative { get; private set; }
public bool IsWhole { get; private set; }

private List<int> wholeDigits;
private List<int> decimalDigits;

其次，我覆蓋了ToString方法，以便數字顯示良好：

public override string ToString()
{
    return string.Format("{0}{1}{2}{3}",
        (IsNegative) ? "-" : "",
        string.Join("", wholeDigits),
        (IsWhole) ? "" : ".",
        (IsWhole) ? "" : string.Join("", decimalDigits));
}

然后，我實現了Equals方法，從而使它們對於數字類型可以按預期工作：

public static bool Equals(LargeDecimal first, LargeDecimal second)
{
    return ReferenceEquals(first, null) 
        ? ReferenceEquals(second, null) 
        : first.Equals(second);
}

public override bool Equals(object obj)
{
    return Equals(obj as LargeDecimal);
}

protected bool Equals(LargeDecimal other)
{
    return CompareTo(other) == 0;
}

public override int GetHashCode()
{
    unchecked
    {
        var hashCode = (wholeDigits != null)
            ? wholeDigits.GetHashCode() 
            : 0;
        hashCode = (hashCode * 397) ^ 
            (decimalDigits != null ? decimalDigits.GetHashCode() : 0);
        hashCode = (hashCode * 397) ^ IsNegative.GetHashCode();
        hashCode = (hashCode * 397) ^ IsWhole.GetHashCode();
        return hashCode;
    }
}

接下來，我添加了一些實用程序方法來幫助完成一些即將發生的任務：

private void ResetToZero()
{
    wholeDigits = new List<int> { 0 };
    decimalDigits = new List<int> { 0 };
    IsWhole = true;
    IsNegative = false;
}

private void NormalizeLists()
{
    RemoveLeadingZeroes(wholeDigits);
    RemoveTrailingZeroes(decimalDigits);
    IsWhole = (decimalDigits.Count == 0 
        || (decimalDigits.Count == 1 && decimalDigits[0] == 0));
}

private void AddLeadingZeroes(List<int> list, int numberOfZeroes)
{
    if (list == null) return;

    for (int i = 0; i < numberOfZeroes; i++)
    {
        list.Insert(0, 0);
    }
}

private void AddTrailingZeroes(List<int> list, int numberOfZeroes)
{
    if (list == null) return;

    for (int i = 0; i < numberOfZeroes; i++)
    {
        list.Add(0);
    }
}

private void RemoveLeadingZeroes(List<int> list, bool leaveOneIfEmpty = true)
{
    if (list == null) return;

    var temp = list;

    for (int i = 0; i < temp.Count; i++)
    {
        if (temp[i] == 0)
        {
            list.RemoveAt(i);
        }
        else
        {
            break;
        }
    }

    if (leaveOneIfEmpty && !list.Any()) list.Add(0);
}

private void RemoveTrailingZeroes(List<int> list, bool leaveOneIfEmpty = true)
{
    if (list == null) return;

    var temp = list;

    for (int i = temp.Count -1; i >= 0; i--)
    {
        if (temp[i] == 0)
        {
            list.RemoveAt(i);
        }
        else
        {
            break;
        }
    }

    if (leaveOneIfEmpty && !list.Any()) list.Add(0);
}

接下來，我添加了一些構造函數。 一個默認值，將數字設置為“ 0”，一個默認值解析一個字符串，另一個LargeDecimal值則從另一個LargeDecimal復制值：

public LargeDecimal() : this("0") { }

public LargeDecimal(string value)
{
    if (value == null) throw new ArgumentNullException("value");

    string number = value.Replace(" ", ""); // remove spaces
    number = number.TrimStart('0'); // remove leading zeroes
    IsNegative = (number.IndexOf('-') == 0); // check for negative
    number = number.Replace("-", ""); // remove dashes
    // add a zero if there were no numbers before a decimal point
    if (number.IndexOf('.') == 0) number = "0" + number; 

    // Initialize lists
    wholeDigits = new List<int>();
    decimalDigits = new List<int>();

    // Get whole and decimal parts of the number
    var numberParts = number.Split(new[] {'.'}, 
        StringSplitOptions.RemoveEmptyEntries);

    IsWhole = numberParts.Length == 1;

    // Add whole digits to the list
    wholeDigits.AddRange(numberParts[0].Select(n => int.Parse(n.ToString())));

    // Add decimal digits to the list (if there are any)
    if (numberParts.Length > 1 && 
        numberParts[1].Sum(n => int.Parse(n.ToString())) > 0)
    {
        numberParts[1] = numberParts[1].TrimEnd('0');
        decimalDigits.AddRange(numberParts[1].Select(n => int.Parse(n.ToString())));
    }

    NormalizeLists();
}

public LargeDecimal(LargeDecimal initializeFrom)
{
    wholeDigits = initializeFrom.wholeDigits
        .GetRange(0, initializeFrom.wholeDigits.Count);
    decimalDigits = initializeFrom.decimalDigits
        .GetRange(0, initializeFrom.decimalDigits.Count);
    IsWhole = initializeFrom.IsWhole;
    IsNegative = initializeFrom.IsNegative;
    NormalizeLists();
}

然后我實現了加減法

public void Add(LargeDecimal other)
{
    if (other == null) return;

    if (IsNegative != other.IsNegative)
    {
        // Get the absolue values of the two operands
        var absThis = new LargeDecimal(this) {IsNegative = false};
        var absOther = new LargeDecimal(other) {IsNegative = false};

        // If the signs are different and the values are the same, reset to 0.
        if (absThis == absOther)
        {
            ResetToZero();
            return;
        }

        // Since the signs are different, we will retain the sign of the larger number
        IsNegative = absThis < absOther ? other.IsNegative : IsNegative;

        // Assign the difference of the two absolute values
        absThis.Subtract(absOther);
        wholeDigits = absThis.wholeDigits.GetRange(0, absThis.wholeDigits.Count);
        decimalDigits = absThis.decimalDigits.GetRange(0, absThis.decimalDigits.Count);
        NormalizeLists();
        return;
    }

    // start with the larger decimal digits list
    var newDecimalDigits = new List<int>();
    newDecimalDigits = decimalDigits.Count > other.decimalDigits.Count
        ? decimalDigits.GetRange(0, decimalDigits.Count)
        : other.decimalDigits.GetRange(0, other.decimalDigits.Count);

    // and add the smaller one to it
    int carry = 0; // Represents the value of the 'tens' digit to carry over
    for (int i = Math.Min(decimalDigits.Count, other.decimalDigits.Count) - 1; i >= 0; i--)
    {
        var result = decimalDigits[i] + other.decimalDigits[i] + carry;
        carry = Convert.ToInt32(Math.Floor((decimal) result / 10));
        result = result % 10;
        newDecimalDigits[i] = result;
    }

    var newWholeDigits = new List<int>();
    newWholeDigits = wholeDigits.Count > other.wholeDigits.Count
        ? wholeDigits.GetRange(0, wholeDigits.Count)
        : other.wholeDigits.GetRange(0, other.wholeDigits.Count);

    for (int i = Math.Min(wholeDigits.Count, other.wholeDigits.Count) - 1; i >= 0; i--)
    {
        var result = wholeDigits[i] + other.wholeDigits[i] + carry;
        carry = Convert.ToInt32(Math.Floor((decimal)result / 10));
        result = result % 10;
        newWholeDigits[i] = result;
    }

    if (carry > 0) newWholeDigits.Insert(0, carry);

    wholeDigits = newWholeDigits.GetRange(0, newWholeDigits.Count);
    decimalDigits = newDecimalDigits.GetRange(0, newDecimalDigits.Count);
    NormalizeLists();
}

public void Subtract(LargeDecimal other)
{
    if (other == null) return;

    // If the other value is the same as this one, then the difference is zero
    if (Equals(other))
    {
        ResetToZero();
        return;
    }

    // Absolute values will be used to determine how we subtract
    var absThis = new LargeDecimal(this) {IsNegative = false};
    var absOther = new LargeDecimal(other) {IsNegative = false};

    // If the signs are different, then the difference will be the sum
    if (IsNegative != other.IsNegative)
    {
        absThis.Add(absOther);
        wholeDigits = absThis.wholeDigits.GetRange(0, absThis.wholeDigits.Count);
        decimalDigits = absThis.decimalDigits.GetRange(0, absThis.decimalDigits.Count);
        NormalizeLists();
        return;
    }

    // Subtract smallNumber from bigNumber to get the difference
    LargeDecimal bigNumber;
    LargeDecimal smallNumber;

    if (absThis < absOther)
    {
        bigNumber = new LargeDecimal(absOther);
        smallNumber = new LargeDecimal(absThis);
    }
    else
    {
        bigNumber = new LargeDecimal(absThis);
        smallNumber = new LargeDecimal(absOther);
    }

    // Pad the whole number and decimal number lists where necessary so that both
    // LargeDecimal objects have the same count of whole and decimal numbers.
    AddTrailingZeroes(
        bigNumber.decimalDigits.Count < smallNumber.decimalDigits.Count
            ? bigNumber.decimalDigits
            : smallNumber.decimalDigits,
        Math.Abs(bigNumber.decimalDigits.Count - smallNumber.decimalDigits.Count));

    AddLeadingZeroes(smallNumber.wholeDigits,
        Math.Abs(bigNumber.wholeDigits.Count - smallNumber.wholeDigits.Count));

    var newWholeDigits = new List<int>();
    var newDecimalDigits = new List<int>();

    bool borrowed = false; // True if we borrowed 1 from next number
    for (int i = bigNumber.decimalDigits.Count - 1; i >= 0; i--)
    {
        if (borrowed)
        {
            bigNumber.decimalDigits[i] -= 1; // We borrowed one from this number last time
            borrowed = false;
        }

        if (bigNumber.decimalDigits[i] < smallNumber.decimalDigits[i])
        {
            bigNumber.decimalDigits[i] += 10; // Borrow from next number and add to this one
            borrowed = true;
        }

        // Since we're working from the back of the list, always add to the front
        newDecimalDigits.Insert(0, bigNumber.decimalDigits[i] - smallNumber.decimalDigits[i]);
    }

    for (int i = bigNumber.wholeDigits.Count - 1; i >= 0; i--)
    {
        if (borrowed)
        {
            bigNumber.wholeDigits[i] -= 1;
            borrowed = false;
        }

        if (bigNumber.wholeDigits[i] < smallNumber.wholeDigits[i])
        {
            bigNumber.wholeDigits[i] += 10;
            borrowed = true;
        }

        newWholeDigits.Insert(0, bigNumber.wholeDigits[i] - smallNumber.wholeDigits[i]);
    }

    if (absThis < absOther) IsNegative = !IsNegative;
    wholeDigits = newWholeDigits.GetRange(0, newWholeDigits.Count);
    decimalDigits = newDecimalDigits.GetRange(0, newDecimalDigits.Count);
    NormalizeLists();
}

最后覆蓋數字運算符：

public static LargeDecimal operator +(LargeDecimal first, LargeDecimal second)
{
    if (first == null) return second;
    if (second == null) return first;

    var result = new LargeDecimal(first);
    result.Add(second);
    return result;
}

public static LargeDecimal operator -(LargeDecimal first, LargeDecimal second)
{
    if (first == null) return second;
    if (second == null) return first;

    var result = new LargeDecimal(first);
    result.Subtract(second);
    return result;
}

public static bool operator >(LargeDecimal first, LargeDecimal second)
{
    if (first == null) return false;
    return first.CompareTo(second) > 0;
}

public static bool operator <(LargeDecimal first, LargeDecimal second)
{
    if (second == null) return false;
    return second.CompareTo(first) > 0;
}

public static bool operator >=(LargeDecimal first, LargeDecimal second)
{
    if (first == null) return false;
    return first.CompareTo(second) >= 0;
}
public static bool operator <=(LargeDecimal first, LargeDecimal second)
{
    if (second == null) return false;
    return second.CompareTo(first) >= 0;
}
public static bool operator ==(LargeDecimal first, LargeDecimal second)
{
    return Equals(first, second);
}

public static bool operator !=(LargeDecimal first, LargeDecimal second)
{
    return !Equals(first, second);
}

感謝您的挑戰！！